2D Geometries

Martineau Solar System Calendars

Tuesday, 1 December 2015 by Bruce Rawles

I just updated this sacred geometry calendar which has images from the fascinating geometric Martineau Solar System models. Here are details about the 12 images which are highly accurate geometric models of pairs of planetary orbits in our solar system. They were inspired by the remarkable work of John Martineau (publisher of Wooden Books), who wrote “A Little Book of Coincidence in the Solar System.” Tiled images of planetary surfaces and related images form the backgrounds. Images are two or more orbits defined by simple 2D (circles, triangles, squares, pentagons, hexagons, octagons) or 3D geometries (e.g. tetrahedron, icosahedron, dodecahedron) typically with 99.9% or greater accuracy. The work picks up where Johannes Kepler’s mystical exploration left off.

Buy the calendar now from Lulu.com

Background Video, Info and Exhibits of the Martineau Solar System

New Coloring Book For Adults in progress

Thursday, 26 November 2015 by Bruce Rawles

Does anyone remember Mandalas Der Heiligen Geometrie (MDHG)? (I still have a few copies of this German edition of my Sacred Geometry Design Sourcebook (SGDS) available, by the way, if anyone in the US would like to buy one; they are currently out of print. Just follow the instructions on this page if you’d like one of the few remaining copies in my inventory.) When I learned that the original German edition master files had been misplaced, I just figured that it had a good run for several years, and mostly put the idea of (laboriously) re-creating the book (for any language) on the proverbial back burner. This past week, however, I’ve been corresponding via email with fellow geometer and author Jay Goldner, who graciously donated his time and effort to make the German version over a decade ago. He was generously both the liaison with the German publisher (and pitched the idea for the book), and did the English-to-German translation as well; kudos to Jay! He is now working again with me in a similar capacity to make an abridged version of MDHG available in Europe (and perhaps elsewhere?) that will be an adult coloring book with a subset of the geometric archetypcal patterns that MDHG and SGDS have featured.

I keep hearing that these coloring books for adults are becoming popular again, which isn’t news for me, but fun to hear. I’ve enjoyed exploring these sacred geometric images artistically with colored pencils, pastels, since the early 1970’s and of course (in more recent decades) digital media and applications. I intentionally made SGDS spiral bound (which took a bit of research to find a good on-demand online printer/fullfillment after printing it locally for years before the online services were more available) so that it’s pages could be laid flat on a photocopy machine or flatbed scanner for making multiple copies for coloring, arts and crafts, enlargements for bigger projects, quilting, stained-glass, and so much more! …

Here are a few similar books … and another example series: Brand New Design Originals-Zentangle 1 Expanded Wrkbk Edition Brand New.

And since I’m (very appropriately) typing this post on Thanksgiving 2015, I want to say a huge THANK YOU to all, for your decades of support and interest in my books, websites, etc. :-)

Online Triangle Calculator and Drawing Tool

Wednesday, 18 November 2015 by Bruce Rawles

Here’s a neat calculator and drawing tool for triangles that works on Google Chrome. Thanks to Jesus S. for sending me the link and the detailed description below! Be sure to try the drawing tool, and checkbox for options such as incircle, circumcircle, etc.

http://TrianCal.esy.es – Open in Google Chrome.
(Triangles online calculator developed by Jesus S.)
YouTube: https://youtu.be/V2IV7lY52mA

I propose this free online calculator triangles without advertising to
help students with geometry, not exercising, because their
calculations formulas are not displayed. It is designed in a didactic
way to check and view the
exercises.

TrianCal is online calculator triangles that works with any
combination of values including sides, heights, angles, the area or
perimeter of any triangle, calculating it with the minimum possible
value (typically three).

Other functions:
– Draw the triangle (s) with GeoGebra.
– Set the range of values allowed into each element.
– The type of angle.
– The type of triangle by its sides and angles.
– Selection of language (English or Spanish).
– Select and angles [degrees (°), Radians, Degrees, minutes and
seconds (°
‘”) or degrees and minutes (°’)] is.
– Number of decimal places to show in the results (0-15).
– You can use the arrow keys and the Tab key to navigate through the
settings.
– Drop-down menu to select values comfortably.
– Create a link (URL) to the current triangle.
– An icon mail to communicate with the author.

NOTE: You must use the Google Chrome browser to display correctly
TrianCal.

Examples of possible combinations:
– The area, perimeter and other data (side, height or angle), if the
outside
equilateral triangle would not need the third data.
– 2 angles and other data (if the value of the other data is not put
aside
the value of “a” at the time of drawing the triangle is 10).
– One hand, one high and one angle.
– 3 heights.
– 3 sides.
– 2 heights and perimeter.
– Any other combination of values.

Beading in 3D, 120-cell 3D printed models and more

Thursday, 12 November 2015 by Bruce Rawles

I received a general question via email from a visitor to GeometryCode.com interested in beading 3-dimensional shapes. Here are the results of my explorations in the process of very quickly researching this question, and my response:

Since your original question was about beading – although many of these may not have geometric aspects of interest – here are some example of 3D beading quite a few example videos of 3D beading that might be helpful.

Since a new dimension is being added (with infinite variations on what can be added to go from 2D to 3D) there are numerous ways to make a 3D pattern from a 2D pattern; these include:

extruding (translation of ) a 2D shape: just making identical copies of the 2D pattern stacked atop each other
rotation or reflection of a 2D shape around either the X or Y (or another axis in the plane of the 2D image)
using other symmetry or symmetries within the 2D object(s) to replicate aspects into the z-axis
countless other variations …

If you already have a 3D image in mind (such as you will find in Sacred Geometry Design Sourcebook on pages 189 (Great Pyramid fold-up model) or Platonic and Archimedean Solids, variations, etc. 196-229 or (space filling polyhedra and close-packing of spheres on page 239, for example) you already have a 3-dimensional pattern to start with. If you have a specific media (such as beading, stained glass, wood-working, welding, Zometool, 3D printing, magnetic spheres, or countless other media variations), you will have other constraints and opportunities to explore. In order to assist further, I would need to know which image on which page in SGDS – since there are over 1300 images in the book! – you have in mind to use for your 3D design.

If you want to make a prototype (or multiple identical copies) you might want to explore 3D printing. There are now somewhat affordable 3D printers, and lots of local 3D printing services. Here’s an example (the “Half of a 120-cell” image on this page) of a 3D-printed geometric shape with kudos to Henry Segerman and Saul Schleimer. Be sure to watch the videos in addition to on this page about the associated images, such as Quintessence (which evidently is also a 3D/4D puzzle/toy which looks wonderful), Triple helix, and Triple gear; fascinating! … and don’t forget to check out the 3D art of Bathsheba who has some exquisite 3D geometric art. :-)

Geometric art and mandalas du jour

Saturday, 31 October 2015 by Bruce Rawles

From the ‘elegant fun’ department: these kinetic sculptures by David C. Roy remind me simultaneously of favorite screen savers, animated crop circles and perhaps a few other moving mandala metaphors for cyclic interactions and relationships with curved arcs, circular and Yin/Yang archetypes; some lovely examples of moving geometry suitable for adorning one’s walls. His site has some engaging videos and other fun stuff on his blog.